Skip to main content
SpringerLink
Log in

Identification of the source function for a seawater intrusion problem in unconfined aquifer

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this work, we study the inverse source problem of a seawater intrusion problem in an unconfined aquifer with sharp-diffuse interfaces. The model associated with the direct problem is nonlinear. We aim to reconstruct the source term following the technique used in [10]. As this technique is based on variable separation, a fixed-point strategy is adopted to linearize the problem. Numerical convergence is proven using some examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Bear, J., Cheng, A.H.D., Sorek, S., Ouazar, D., Herrera, I. (eds.): Concepts, Methods and Practices, Kluwer Academic Pub. Springer, Berlin (1999)

    Google Scholar 

  2. Choquet, C., Diedhiou, M.M., Rosier, C.: Seawater intrusion problem in a free aquifer : derivation of a sharp-diffuse interfaces model and existence result. SIAM J. Appl. 76(1), 138–158 (2016)

    Article  MathSciNet  Google Scholar 

  3. Choquet, C., Diédhiou, M.M., Rosier, C.: Mathematical analysis of a sharp–diffuse interfaces model for seawater intrusion. Journal of Differential Equations 259(8), 3803–3824 (2015)

    Article  MathSciNet  Google Scholar 

  4. Choquet, C., Ji-Li, C.: Rosier, global existence for seawater intrusion models: comparison between sharp interface and sharp-diffuse interface approaches (126), 1–27 (2015)

  5. Choquet, C., Ji-Li, C.: Rosier, uniqueness for cross-diffusion systems issuing from saltwater intrusion problems. EJDE 2017(256), 1–22 (2017)

    Google Scholar 

  6. Hansen, C., Jensen, T.K., Rodriguez, G.: An adaptive pruning algorithm for the discrete L-curve criterion. Journal of Computational and Applied Mathematics 198, 483–492 (2007)

    Article  MathSciNet  Google Scholar 

  7. Gagneux, G., Madaune-Tort, M.: Analyse mathématique de modèles non linéaires de l’ingénierie pétrolière. Math. Appl. 22. Springer (1996)

  8. Fatullayev, A.G.: Numerical solution of the inverse problem of determining an unknown source term in a heat equation. Mathematics and Computers in Simulation 58, 247–253 (2002)

    Article  MathSciNet  Google Scholar 

  9. Fatullayev, A.G.: Numerical solution of the inverse problem of determining an unknown source term in a two-dimensional heat equation. Appl. Math. Comput. 152, 659–666 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Kulbay, M., Mukanova, B., Sebu, C.: Identification of separable sources for advection-diffusion equations with variable diffusion coefficient from boundary measured data, Inverse problems in science and engineering 1741-5977-March (2016)

  11. Lions, J.L., Magenes, E.: Problèmes aux limites non homogènes, vol. 1 Dunod (1968)

  12. Moustapha, H.: ÉTude du problème inverse d’un modèle d’intrusion saline thèse doctorale 12 Mars (2015)

  13. Mourad, A., Rosier, C.: A nonlinear optimization method applied to the hydraulic conductivity identification in unconfined aquifers. J. Optim. Theory Appl. 183, 705–730 (2019)

    Article  MathSciNet  Google Scholar 

  14. Mukanova, B., Vladimir, G.: Romanov, inverse source problem for wave equation and GPR data interpretation problem (2016)

  15. Najib, K., Rosier, C.: On the global existence for a degenerate elliptic–parabolic seawater intrusion problem. Math. Comput. Simul. 81(10), 2282–2295 (2011)

    Article  MathSciNet  Google Scholar 

  16. Simon, J.: Compact sets in the space lp(0, t, b). Annali di Matematica pura ed applicata (IV) CXLVI, pp. 65–96 (1987)

  17. Tber, M.H., El Alaoui Talibi, M.: A finite element method for hydraulic conductivity identification in a seawater intrusion problem. Comput. Geosci. 33, 860–874 (2007)

    Article  Google Scholar 

  18. Tber, M.H., El Alaoui Talibi, M., Ouazar, D.: Parameters identification in a seawater intrusion model using adjoint sensitive method. Math. Comput. Simul. 77, 301–312 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LERMA, Ecole Mohammadia d’Ingénieurs, Université Mohammed V, Agdal-Rabat, Morocco

    S. Slimani, I. Medarhri & K. Najib

  2. Ecole Nationale Supérieure des Mines de Rabat, Agdal, 1000, Morocco

    I. Medarhri & K. Najib

  3. Institute Camille Jordan, Ecole centrale lyon, Écully, 69134, France

    A. Zine

Authors
  1. S. Slimani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Medarhri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. Najib
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Zine
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Slimani.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slimani, S., Medarhri, I., Najib, K. et al. Identification of the source function for a seawater intrusion problem in unconfined aquifer. Numer Algor 84, 1565–1587 (2020). https://doi.org/10.1007/s11075-020-00925-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-020-00925-6

Keywords

Search

Navigation